On residual nilpotence of group extensions

On residual nilpotence of group extensions Full article

Journal

International Journal of Algebra and Computation
ISSN: 0218-1967 , E-ISSN: 1793-6500

Output data

Year: 2023, Volume: 33, Number: 8, Pages: 1617-1650 Pages count : 34 DOI: 10.1142/s0218196723500613

Tags

Residually nilpotent group, group extension, semi-direct product, free-by-infinite cyclic group

Authors

Bardakov Valeriy G. ^1,2 , Bryukhanov O.V. ³ , Нещадим М.В. ¹

Affiliations

1	Novosibirsk State Agrarian University, Dobrolyubova Street, 160 Novosibirsk 630039, Russia
2	Sobolev Institute of Mathematics, Prosp. Koptyuga 4, Novosibirsk 630090, Russia
3	Novosibirsk State Technical University, 20 K. Marksa Ave. Novosibirsk 630073, Russia

We study the following question: under what conditions extension of one residuallynilpotent group by another residually nilpotent group is residually nilpotent? We provesome suﬃcient conditions under which this extension is residually nilpotent. Also, westudy this question for semi-direct products and, in particular, for extensions of freegroup by inﬁnite cyclic group: Fn ϕ Z. We ﬁnd conditions under which this group isresidually nilpotent, ﬁnd conditions under which this group has long lower central series.In particular, we prove that for n = 2 the length of the lower central series of Fn ϕ Zis equal to 2, ω or ω2

Bardakov V.G. , Bryukhanov O.V. , Нещадим М.В.
On residual nilpotence of group extensions
International Journal of Algebra and Computation. 2023. V.33. N8. P.1617-1650. DOI: 10.1142/s0218196723500613 WOS Scopus РИНЦ OpenAlex

Submitted:	Aug 24, 2021
Accepted:	Aug 9, 2023
Published print:	Sep 22, 2023
Published online:	Sep 22, 2023

Web of science:	WOS:001074880800001
Scopus:	2-s2.0-85172930776
Elibrary:	63016562
OpenAlex:	W4386000756

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